G. Cowan RHUL Physics Status of Higgs combination page 1 Status of Higgs Combination ATLAS Higgs Meeting CERN/phone, 7 November, 2008 Glen Cowan, RHUL Eilam Gross, Weizmann Instutite

G. Cowan RHUL Physics Status of Higgs combination page 2 Outline 1)Overview of HG11 goals, people involved, documents 2)Review of combination method 3)Validation of approximations used 4)Results of combination 5)Summary

G. Cowan RHUL Physics Status of Higgs combination page 3 CSC HG11 Overview Describes statistical methods for combination of search channels. Applies combination to (a subset of) Higgs channels: WW→e  (0-jet and 2-jet), , ,  ZZ(*)→4l Treats systematics by means of profile likelihood method. Considers fixed-mass hypothesis; look-elsewhere-effect must be studied separately. NB  and WW CSC notes describe floating-mass fits. Some approximations used for discovery/exclusion significance. Valid for L > 2 fb . For lower L need toy MC methods. Does not represent final word on methods -- other developments ongoing (Bayesian, CLs, look-elsewhere-effect,...)

G. Cowan RHUL Physics Status of Higgs combination page 4 CSC HG11 People Editors: Eilam Gross, Glen Cowan Contacts for individual channels: WWBill Quayle  Yaquan Fang  Kyle Cranmer 4lAndrea Di Simone Note referee:Fabiola Gianotti Chapter referees:Fabio Cerutti, Bruno Mansoulie Chapter editors:Rachid Mazini, Bill Murray + e.g. Louis Fayard, Aleandro Nisati, Karl Jakobs, Dave Charlton, Ofer Vitells...

G. Cowan RHUL Physics Status of Higgs combination page 5 HG11 Documents Source of note in CVS: AFS area for combination inputs: /afs/cern.ch/atlas/project/statistics/ The draft note circulated to collaboration (old WW numbers): ATL-COM-PHYS , higgs_combo_csc_3nov08.pdf The draft note (new WW numbers) 4 November 2008 version: higgs_combo_csc_4nov08.pdf

G. Cowan RHUL Physics Status of Higgs combination page 6 Reminder of combination method  represents all nuisance parameters, e.g., background rate, shapes  =1 is SM.  =0 is background only. The single-channel likelihood function uses Poisson model for events in signal and control histograms: There is a likelihood L i ( ,  i ) for each channel, i = 1, …, N. The full likelihood function is

G. Cowan RHUL Physics Status of Higgs combination page 7 Profile likelihood ratio To test hypothesized value of , construct profile likelihood ratio: Maximized L for given  Maximized L Equivalently use q  =  2 ln (  ): data agree well with hypothesized  → q  small data disagree with hypothesized  → q  large

G. Cowan RHUL Physics Status of Higgs combination page 8 p-value / significance of hypothesized  Test hypothesized  by giving p-value, probability to see data with ≤ compatibility with  compared to data observed: Equivalently use significance:

G. Cowan RHUL Physics Status of Higgs combination page 9 Sampling distribution of q  To compute p-value of hypothesized , need distribution f (q  |  ). For 5  discovery we need a p-value of 2.8 × 10  ; To estimate this using MC needs > 10 8 events. Wilk’s theorem: in large sample limit f (q  |  ) should approach with w = ½. (a “half-chi-square” distribution). Validation exercise shows approximation OK for L ≥ 2 fb . We use the half-chi-square approximation in the current note; for lower luminosities we will need MC to get f (q  |  ) (feasible for exclusion limits at 95% CL).

G. Cowan RHUL Physics Status of Higgs combination page 10 Example from validation exercise: ZZ (*) → 4l 5  level (One minus) cumulative distributions. Band gives 68% CL limits. ½2½2 ½2½2 ½2½2 ½2½2 Distributions of q 0 for 2, 10 fb  from MC compared to ½  2

G. Cowan RHUL Physics Status of Higgs combination page 11 Special treatment for WW+0j discovery For WW (→ Bill Quayle), further systematic studies were carried out that went beyond profile likelihood method. Parameter variations were considered to minimize the sensitivity of the q  distribution to variations in other fixed parameters such as QCD scale. For WW0j discovery (  =0), the parameter alterations led to a distribution of q 0 significantly different from expected form. original parameters altered parameters

G. Cowan RHUL Physics Status of Higgs combination page 12 Special treatment for WW+0j discovery (2) So for WW0j discovery (  =0), the p-values were determined by toy MC and transformed to effective q 0 values according to which was then used in the formula for the median significance.

G. Cowan RHUL Physics Status of Higgs combination page 13 Sensitivity Discovery: Generate data under s+b (  = 1) hypothesis; Test hypothesis  = 0 → p-value → Z. Exclusion: Generate data under background-only (  = 0) hypothesis; Test hypothesis . If  = 1 has p-value < 0.05 exclude m H at 95% CL. Estimate median significance by setting data equal to expectation values (Asimov data) or by using MC. For median, can combine significances of individual channels. For significance of e.g. a real data set, need global fit.

G. Cowan RHUL Physics Status of Higgs combination page 14 Combined discovery sensitivity No WW0j spin correlations With WW0j spin correlations

G. Cowan RHUL Physics Status of Higgs combination page 15 Combined discovery sensitivity No WW0j spin correlations With WW0j spin correlations

G. Cowan RHUL Physics Status of Higgs combination page 16 Combined discovery sensitivity No WW0j spin correlations With WW0j spin correlations Shaded band below 2 fb  indicates this region not accurate (but expected to be conservative).

G. Cowan RHUL Physics Status of Higgs combination page 17 p-value of  =1 (SM) versus m H No WW0j spin correlations With WW0j spin correlations

G. Cowan RHUL Physics Status of Higgs combination page 18 p-value of  =1 (SM) versus m H No WW0j spin correlations With WW0j spin correlations

G. Cowan RHUL Physics Status of Higgs combination page 19  p-value of  =1 (SM) versus L, m H No WW0j spin correlations With WW0j spin correlations Shaded band below 2 fb  indicates this region not accurate (but expected to be conservative).

G. Cowan RHUL Physics Status of Higgs combination page 20 Median 95% CL limit on  assuming no Higgs

G. Cowan RHUL Physics Status of Higgs combination page 21 Summary Combination method based on developed and applied to: WW→e  (0-jet and 2-jet), , ,  ZZ(*)→4l Systematics incorporated using profile likelihood ratio. Work represents a “snapshot” of combination activities; other areas still ongoing activity (Bayesian, CLs, look-elsewhere-effect…) Approximations used expected to be valid for L ≥ 2 fb . For 2 fb  : expected (median) sensitivity is ≥5  for discovery of a Higgs in the mass range between 143 and 179 GeV; expected upper limit at 95% CL on m H is 121 GeV.

G. Cowan RHUL Physics Status of Higgs combination page 22 Summary (2) Many comments by referees (and others) -- led to important improvements: More thorough explanation of mathematical approximations used and of their limitations. Comparison with methods used at LEP (appendix). Careful formulation of conclusions, e.g., results conservative as only subset of channels used; caveats concerning approximations; L < 2 fb  will need toy MC studies. Draft circulated to collaboration does not yet have WW spin correlations; these give improved sensitivity but no change in basic conclusions.

G. Cowan RHUL Physics Status of Higgs combination page 23 Extra slides

G. Cowan RHUL Physics Status of Higgs combination page 24 Expected discovery significance from WW0j with spin correlations no spin correlations

G. Cowan RHUL Physics Status of Higgs combination page 25 Luminosity for 5  discovery assuming SM Higgs

G. Cowan RHUL Physics Status of Higgs combination page 26 Luminosity for 95% CL exclusion

G. Cowan RHUL Physics Status of Higgs combination page 27 Median 95% CL limit on  assuming no Higgs